Understanding Standard Normal Distribution and Z-Scores

The video tutorial explains how to find a Z-score for a standard normal distribution where the probability of Z being less than a certain value C equals 0.614. It discusses the concept of Z-scores, their relation to probability, and how to use the TI84 calculator's inverse norm feature to find the Z-score. The tutorial provides step-by-step instructions for entering the probability into the calculator and obtaining the Z-score, which is approximately 0.2898.

What is the main goal when working with a standard normal distribution in this context?

• To find a Z-score for a given probability

• To determine the standard deviation

• To find the mean of the distribution

• To calculate the median of the data

Why is the Z-score expected to be positive when the probability is greater than 0.5?

• Because the standard deviation is positive

• Because the area to the left is more than half

• Because the data is skewed to the right

• Because the mean is always positive

What feature of the TI84 calculator is used to find the Z-score for a given probability?

• Mean Calculation

• Standard Deviation

• Inverse Norm

• Normal CDF

When using the inverse norm feature on the TI84, what values are assumed for the mean and standard deviation in a standard normal distribution?

• Mean = 1, Standard Deviation = 0

• Mean = 0, Standard Deviation = 1

• Mean = 0.5, Standard Deviation = 0.5

• Mean = 1, Standard Deviation = 1

What is the calculated Z-score rounded to four decimal places for the given probability of 0.614?

• 0.5000

• 0.7500

• 0.6140

• 0.2898